in 1980,median family income was about $17,000 and in 2000 it was about $42,000.
a) find the slope of the passing through the points(1980,17000) &(2000,42000)
b)Interpret the slope as a rate of change
c)If this trend continues,estimate the median family income in 2005

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in 1980,median family income was about $17,000 and in 2000 it was about $42,000.
a) find the slope of the passing through the points(1980,17000) &(2000,42000)
b)Interpret the slope as a rate of change
c)If this trend continues,estimate the median family income in 2005

Mathematics

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tkhunny

5 years ago

Well, do it! What do you get of a)?

anonymous

5 years ago

25000 @tkhunny

tkhunny

5 years ago

That doesn't quite make sense. 42000 - 17000 = 25000. Okay, I see where that came from, but a SLOPE is a UNIT measure. We do not need only the difference in income, 25000, we need the difference in years gone by.
\(\dfrac{42000 - 17000}{2000-1980}\) dollars / year

If we have a concept of "slope", we must have reference to a Cartesian Coordinate system. In this case, the x-axis should be labeled "year" and the y-axis "median family income". Thus the units on the x-axis are measured in years and the units on the y-axis are measured in dollars.
When we then speak of the slope, we have a concept that compares the y-axis units to the x-axis units. Therefore, on this graph, the units of slope are "dollars per year".
Make any sense at all? I was rambling a bit.

anonymous

5 years ago

@tkhunny kind of

anonymous

5 years ago

im still lost a bit

tkhunny

5 years ago

Concept: Linear Equations
We're not just drawing lines on paper. We're trying to learn something. We're trying to see and examine relationships between two things.
Current Problem:
Year vs. Median Income.
How has median income changed over the years? Let's plot a few points on a Cartesian coordinate system and see if there is a linear relationship.
Since we have been studying linear equations and their graphs, we can use all of our graphing skill and maybe learn something new.
We have: (1980,17000) and (2000,42000)
Okay, it looks like median income might be increasing over the years. How fast might it be increasing? Well, we have ($42000 - $17000)/(2000 yrs - 1980 yrs) = 25000/20 ($/yr) = $1250 / year.
Oh, I see. Maybe we can believe that Median Income increases $1250 per year. Can we create an equation so that we can see what the Median Income might have been on other years that we were not able to tabulate?
Again, we studied linear equations, so we know how to draw a graph if we can define a Cartesian Coordinate system and then gather enough information to define a unique line.
x-axis Years
y-axis Median Family Income
I see it now. We have a point (1980,17000) and we have a slope ($1250/yr). Let's use the Point=Slope form of a line and we will have our equation!
(y-k) = m(x-h)
The point we have is (h.k) = (1980 yrs,$17000). Let's substitute that.
(y - 17000) = m(x - 1980)
We calculated the slope in our previous discovery. Substitute that.
(y - 17000) = (1250)(x - 1980)
There is the line we need. Put that in a more useful form and you'll nearly be done.
Now how about it? Did the thought-process narrative do you any good?

anonymous

5 years ago

so the income increased 1250.00 yearly right @tkhunny

tkhunny

5 years ago

Kind of. All we REALLY know is the two points. What ACTUALLY happened in the middle is not really known. We are ASSUMING that it is a linear relationship. The best we can say is that the AVERAGE change over that period was $1250 / year.